Geodesic
Bridgeland-stable moduli spaces for $K$-trivial surfaces
Journal of the European Mathematical Society, Tome 15 (2013) no. 1, pp. 1-38

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We give a one-parameter family of Bridgeland stability conditions on the derived category of a smooth projective complex surface S and describe "wall-crossing behavior'' for objects with the same invariants as OC​(H) when H generates Pic(S) and C∈∣H∣. If, in addition, S is a K3 or Abelian surface, we use this description to construct a sequence of fine moduli spaces of Bridgeland-stable objects via Mukai flops and generalized elementary modifications of the universal coherent sheaf. We also discover a natural generalization of Thaddeus' stable pairs for curves embedded in the moduli spaces.
DOI : 10.4171/jems/354
Classification : 57-XX, 00-XX
Keywords: 
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     title = {Bridgeland-stable moduli spaces for $K$-trivial surfaces},
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Daniele Arcara; Aaron Bertram. Bridgeland-stable moduli spaces for $K$-trivial surfaces. Journal of the European Mathematical Society, Tome 15 (2013) no. 1, pp. 1-38. doi: 10.4171/jems/354

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